Finite Group Databasebeta

← C103×#19194 #39924469

Subgroups — C103×#19194 #39924469

Order 26368.

638 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C103×#3246C212yesmaximal
2C103×#3160C211yesmaximal, characteristic, complemented
3C103×#2931C211yesmaximal, characteristic
4C103×#1695C212yesmaximal, complemented
5C103×#1693C212yesmaximal, complemented
6C103×#1671C214yesmaximal, complemented
7C2×#334×C103C211yesmaximal, characteristic, complemented
8C103×#1550C212yesmaximal, complemented
9C2×#131×C103—21no—
10#533×C103C2212yes—
11#532×C103C2211yescharacteristic
12#500×C103C2211yescharacteristic
13#500×C103C2211yescharacteristic
14#499×C103—21no—
15#499×C103—21no—
16#498×C103C2212yes—
17#476×C103C2214yes—
18#475×C103—22no—
19#465×C103—24no—
20#461×C103C2214yes—
21#460×C103—22no—
22#436×C103—21no—
23#436×C103C2212yes—
24C8×D4×C103—21no—
25C8×D4×C103C2212yes—
26#427×C103—21no—
27#427×C103—21no—
28#423×C103C2211yescharacteristic
29C2×C4⋊C8×C103C2212yes—
30#408×C103—21no—
31C2×C4×C8×C103C2211yescharacteristic
32#334×C103C2212yes—
33#334×C103C2212yes—
34#333×C103C2214yes—
35#332×C103C2214yes—
36C2×#41×C103—21no—
37C2×SD16×C103—24no—
38#131×C103—44no—
39C2×M16×C103—21no—
40C2×M16×C103—22no—
41C22×C8×C103—22no—
42C22×C8×C103—22no—
43C22×C8×C103D411yescharacteristic
44C22×C8×C103D411yescharacteristic
45C4⋊Q8×C103D411yescharacteristic
46C4⋊Q8×C103C2312yes—
47C4⋊Q8×C103C2312yes—
48#127×C103D411yescharacteristic
49#125×C103—22no—
50#124×C103—21no—
51C22⋊Q8×C103—22no—
52C22⋊Q8×C103—22no—
53#121×C103—21no—
54#121×C103D412yes—
55C4×Q8×C103—22no—
56C4×Q8×C103—22no—
57C4×D4×C103—21no—
58C4×D4×C103C2312yes—
59#117×C103—22no—
60C2×C42×C103C2311yescharacteristic
61#107×C103—21no—
62#107×C103—21no—
63#107×C103—21no—
64#107×C103—21no—
65#106×C103—22no—
66#106×C103—22no—
67#106×C103—24no—
68C4⋊C8×C103—22no—
69C4⋊C8×C103—21no—
70C4⋊C8×C103C2314yes—
71C4⋊C8×C103C2312yes—
72#103×C103—24no—
73#102×C103—24no—
74C22⋊C8×C103—22no—
75C22⋊C8×C103—22no—
76C4×C8×C103D411yescharacteristic
77C4×C8×C103D411yescharacteristic
78C4×C8×C103C2311yescharacteristic
79C4×C8×C103C2311yescharacteristic
80#41×C103—42no—
81#41×C103—42no—
82C2×Q8×C103—21no—
83C2×Q8×C103—22no—
84C2×Q8×C103—22no—
85C2×D4×C103—22no—
86C2×D4×C103—21no—
87C2×D4×C103—21no—
88C2×D4×C103C2×D412yes—
89C22×C4×C103—22no—
90C22×C4×C103C2×D411yescharacteristic
91C22×C4×C103C2×D411yescharacteristic
92C22×C4×C103#4111yescharacteristic
93SD16×C103—84no—
94M16×C103—42no—
95M16×C103—44no—
96C2×C8×C103—22no—
97C2×C8×C103—22no—
98C2×C8×C103—24no—
99C2×C8×C103—44no—
100C2×C8×C103—82no—
101C2×C8×C103SD1614yescomplemented
102C2×C8×C103C2×D411yescharacteristic
103C2×C8×C103C2×D411yescharacteristic
104C2×C8×C103C2×D411yescharacteristic
105C2×C8×C103C2×D411yescharacteristic
106C4⋊C4×C103—21no—
107C4⋊C4×C103—22no—
108C4⋊C4×C103—22no—
109C4⋊C4×C103—22no—
110C4⋊C4×C103—22no—
111C4⋊C4×C103—42no—
112C4⋊C4×C103—42no—
113C4⋊C4×C103C2×D412yes—
114C22⋊C4×C103—22no—
115C22⋊C4×C103—22no—
116C22⋊C4×C103—42no—
117C42×C103—42no—
118C42×C103C2×D411yescharacteristic
119C42×C103C2×D411yescharacteristic
120C42×C103#4111yescharacteristic
121C42×C103C2411yescharacteristic
122C23×C103—22no—
123C23×C103#12111yescharacteristic
124Q8×C103—42no—
125Q8×C103—42no—
126Q8×C103—42no—
127Q8×C103—82no—
128D4×C103—24no—
129D4×C103—42no—
130D4×C103—44no—
131D4×C103—42no—
132C2×C4×C103—22no—
133C2×C4×C103—22no—
134C2×C4×C103—41no—
135C2×C4×C103—42no—
136C2×C4×C103—42no—
137C2×C4×C103—42no—
138C2×C4×C103—42no—
139C2×C4×C103#12111yescharacteristic
140C2×C4×C103#12111yescharacteristic
141C2×C4×C103#12111yescharacteristic
142C2×C4×C103C2×SD1612yes—
143C2×C4×C103#13712yes—
144C2×C4×C103C22×D411yescharacteristic
145C2×C4×C103C22×D411yescharacteristic
146C2×C4×C103C2×#4111yescharacteristic
147C8×C103—21no—
148C8×C103—21no—
149C8×C103—42no—
150C8×C103—44no—
151C8×C103C2×SD1612yes—
152C8×C103C2×SD1612yes—
153C22×C103—21no—
154C22×C103—21no—
155C22×C103—42no—
156C22×C103—42no—
157C22×C103—42no—
158C22×C103#46112yes—
159C22×C103C2×#12111yescharacteristic
160C4×C103—21no—
161C4×C103—21no—
162C4×C103—21no—
163C4×C103—42no—
164C4×C103—82no—
165C4×C103—82no—
166C4×C103#46112yes—
167C4×C103C22×SD1611yescharacteristic
168C4×C103C2×#13711yescharacteristic
169C4×C103#57712yes—
170#19194C10311yesmaximal, characteristic, direct product factor, Sylow
171C2×C103—22no—
172C2×C103—82no—
173C2×C103C2×#46111yescharacteristic
174C2×C103#306011yescharacteristic
175C2×C103#306711yescharacteristic
176#3246C2×C10312yes—
177#3160C2×C10311yescharacteristic, complemented
178#2931C2×C10311yescharacteristic
179#1695C2×C10312yescomplemented
180#1693C2×C10312yescomplemented
181#1671C2×C10314yescomplemented
182C2×#334C2×C10311yescharacteristic, complemented
183#1550C2×C10312yescomplemented
184C103#1919411yescharacteristic, direct product factor, Sylow
185C2×#131—21no—
186#533C22×C10312yes—
187#532C22×C10311yescharacteristic
188#500C22×C10311yescharacteristic
189#500C22×C10311yescharacteristic
190#499—21no—
191#499—21no—
192#498C22×C10312yes—
193#476C22×C10314yes—
194#475—22no—
195#465—24no—
196#461C22×C10314yes—
197#460—22no—
198#436—21no—
199#436C22×C10312yes—
200C8×D4—21no—
201C8×D4C22×C10312yes—
202#427—21no—
203#427—21no—
204#423C22×C10311yescharacteristic
205C2×C4⋊C8C22×C10312yes—
206#408—21no—
207C2×C4×C8C22×C10311yescharacteristic
208#334C22×C10312yes—
209#334C22×C10312yes—
210#333C22×C10314yes—
211#332C22×C10314yes—
212C2×#41—21no—
213C2×SD16—24no—
214#131—44no—
215C2×M16—21no—
216C2×M16—22no—
217C22×C8—22no—
218C22×C8—22no—
219C22×C8D4×C10311yescharacteristic
220C22×C8D4×C10311yescharacteristic
221C4⋊Q8D4×C10311yescharacteristic
222C4⋊Q8C23×C10312yes—
223C4⋊Q8C23×C10312yes—
224#127D4×C10311yescharacteristic
225#125—22no—
226#124—21no—
227C22⋊Q8—22no—
228C22⋊Q8—22no—
229#121—21no—
230#121D4×C10312yes—
231C4×Q8—22no—
232C4×Q8—22no—
233C4×D4—21no—
234C4×D4C23×C10312yes—
235#117—22no—
236C2×C42C23×C10311yescharacteristic
237#107—21no—
238#107—21no—
239#107—21no—
240#107—21no—
241#106—22no—
242#106—22no—
243#106—24no—
244C4⋊C8—22no—
245C4⋊C8—21no—
246C4⋊C8C23×C10312yes—
247C4⋊C8C23×C10314yes—
248#103—24no—
249#102—24no—
250C22⋊C8—22no—
251C22⋊C8—22no—
252C4×C8D4×C10311yescharacteristic
253C4×C8D4×C10311yescharacteristic
254C4×C8C23×C10311yescharacteristic
255C4×C8C23×C10311yescharacteristic
256#41—42no—
257#41—42no—
258C2×Q8—21no—
259C2×Q8—22no—
260C2×Q8—22no—
261C2×D4—22no—
262C2×D4—21no—
263C2×D4—21no—
264C2×D4C2×D4×C10312yes—
265C22×C4—22no—
266C22×C4C2×D4×C10311yescharacteristic
267C22×C4C2×D4×C10311yescharacteristic
268C22×C4#41×C10311yescharacteristic
269SD16—84no—
270M16—42no—
271M16—44no—
272C2×C8—22no—
273C2×C8—22no—
274C2×C8—24no—
275C2×C8—44no—
276C2×C8—82no—
277C2×C8SD16×C10314yescomplemented
278C2×C8C2×D4×C10311yescharacteristic
279C2×C8C2×D4×C10311yescharacteristic
280C2×C8C2×D4×C10311yescharacteristic
281C2×C8C2×D4×C10311yescharacteristic
282C4⋊C4—21no—
283C4⋊C4—22no—
284C4⋊C4—22no—
285C4⋊C4—22no—
286C4⋊C4—22no—
287C4⋊C4—42no—
288C4⋊C4—42no—
289C4⋊C4C2×D4×C10312yes—
290C22⋊C4—22no—
291C22⋊C4—22no—
292C22⋊C4—42no—
293C42—42no—
294C42C2×D4×C10311yescharacteristic
295C42C2×D4×C10311yescharacteristic
296C42#41×C10311yescharacteristic
297C42C24×C10311yescharacteristic
298C23—22no—
299C23#121×C10311yescharacteristic
300Q8—42no—
301Q8—42no—
302Q8—42no—
303Q8—82no—
304D4—24no—
305D4—42no—
306D4—44no—
307D4—42no—
308C2×C4—22no—
309C2×C4—22no—
310C2×C4—41no—
311C2×C4—42no—
312C2×C4—42no—
313C2×C4—42no—
314C2×C4—42no—
315C2×C4#121×C10311yescharacteristic
316C2×C4#121×C10311yescharacteristic
317C2×C4#121×C10311yescharacteristic
318C2×C4C2×SD16×C10312yes—
319C2×C4#137×C10312yes—
320C2×C4C22×D4×C10311yescharacteristic
321C2×C4C22×D4×C10311yescharacteristic
322C2×C4C2×#41×C10311yescharacteristic
323C8—21no—
324C8—21no—
325C8—42no—
326C8—44no—
327C8C2×SD16×C10312yes—
328C8C2×SD16×C10312yes—
329C22—21no—
330C22—21no—
331C22—42no—
332C22—42no—
333C22—42no—
334C22#461×C10312yes—
335C22C2×#121×C10311yescharacteristic
336C4—21no—
337C4—21no—
338C4—21no—
339C4—42no—
340C4—82no—
341C4—82no—
342C4#461×C10312yes—
343C4C22×SD16×C10311yescharacteristic
344C4C2×#137×C10311yescharacteristic
345C4#577×C10312yes—
346C2—22no—
347C2—82no—
348C2C2×#461×C10311yescharacteristic
349C2C103×#306011yescharacteristic
350C2C103×#306711yescharacteristic
subgroupG/H
center, socleC22×C103C2×#121
commutator, Frattini, cosocleC42C24×C103
prime radical#532×C103C22
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C103 ◁ C2×C42×C103 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C103×#3160C2semidirect
4. C103×#1695C2semidirect
5. C103×#1693C2semidirect
6. C103×#1671C2semidirect
7. C2×#334×C103C2semidirect
8. C103×#1550C2semidirect
101. C2×C8×C103SD16semidirect
170. #19194C103direct (N × H)
177. #3160C2×C103semidirect
179. #1695C2×C103semidirect
180. #1693C2×C103semidirect
181. #1671C2×C103semidirect
182. C2×#334C2×C103semidirect
183. #1550C2×C103semidirect
184. C103#19194direct (N × H)
277. C2×C8SD16×C103semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C103×#32462
C103×#31602
C103×#29312
C103×#16952
C103×#16932
C103×#16712
C2×#334×C1032
C103×#15502
#19194103